MHB Can Matlab or Python find a solution to this complex nonlinear equation?

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The discussion centers on solving a complex nonlinear equation involving arcsine functions and a variable 'a'. Initial attempts using Mathematica's NSolve and Solve failed, but FindRoot provided a result near a=5000. However, further analysis indicates that a=5000 is not a valid solution, as graphing suggests the equation approaches zero only as 'a' approaches infinity. The rounding and truncation in FindRoot may have led to this misleading result. The participants are seeking alternative methods in Matlab or Python to find a more accurate solution.
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I let Mathematica run for over an hour but it couldn't solve this equation. Can someone run this in Matlab or Python and see if they can get a solution?

$\alpha = 2\arcsin\left(\sqrt{\frac{10014.6}{2*a}}\right)$
$\beta = 2\arcsin\left(\sqrt{\frac{10014.6 - 6339.06}{2*a}}\right)$

$$
780\sqrt{\frac{398600}{a^3}} = \alpha - \beta -(\sin(\alpha) - \sin(\beta))
$$
Solving for a.

Never mind. NSolve and Solve won't work but FindRoot did for {a,5000}.
 
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dwsmith said:
I let Mathematica run for over an hour but it couldn't solve this equation. Can someone run this in Matlab or Python and see if they can get a solution?

$\alpha = 2\arcsin\left(\sqrt{\frac{10014.6}{2*a}}\right)$
$\beta = 2\arcsin\left(\sqrt{\frac{10014.6 - 6339.06}{2*a}}\right)$

$$
780\sqrt{\frac{398600}{a^3}} = \alpha - \beta -(\sin(\alpha) - \sin(\beta))
$$
Solving for a.

Never mind. NSolve and Solve won't work but FindRoot did for {a,5000}.

a=5000 is not a solution.
Graphing it with Wolfram suggests that it will only be zero if $a \to \infty$.
FindRoot is probably doing some rounding and truncation.
 
I like Serena said:
a=5000 is not a solution.
Graphing it with Wolfram suggests that it will only be zero if $a \to \infty$.
FindRoot is probably doing some rounding and truncation.

{a,5000} means look for a solution beyound 5000
 

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